To make an estimate of the splitting between the Cooper-pair formation temperature, \(T_{pair}\) , and the actual superconducting transition temperature, \(T_c\) , we followed Ref.[1]} and consider a simplified interacting two-band model in two dimensions with hole and electron pockets with small Fermi energies (\(E_{F}^h =20\) meV and \(E_{F}^e =10\) meV) as depicted in the Fig.REF (a). As we are interested in the evolution of the FeSe system as a function of the Sulfur doping we assumed the system is orthorhombic. However, once the intraband interaction in the \(d\) -wave interaction dominates and the \(s-\) wave component of the gap is small the results can be easily extrapolated to the purely tetragonal system. The Hamiltonian reads
\(\begin{split}\hat{H} = & \sum _{\textbf {k}\alpha \sigma }\xi _{\textbf {k}\alpha }c^\dagger _{\alpha \textbf {k}\sigma }c_{\alpha \textbf {k}\sigma } \\&+ \sum _{\textbf {k},\textbf {k}^\prime ,\alpha ,\alpha ^\prime }U_{\alpha \alpha ^\prime }(\textbf {k}\textbf {k}^\prime )c^\dagger _{\alpha \textbf {k}\uparrow }c^\dagger _{\alpha -\textbf {k}\downarrow }c_{\alpha ^\prime -\textbf {k}^\prime \downarrow }c_{\alpha ^\prime \textbf {k}^\prime \uparrow }\end{split}\) 
